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The Seebeck effect is used in thermoelectric generators (TEGs) to supply electronic circuits by converting the waste thermal into electrical energy. This generated electrical power is directly proportional to the temperature difference between the TEG module's hot and cold sides. Depending on the applications, TEGs can be used either under constant temperature gradient between heat reservoirs or constant heat flow conditions. Moreover, the generated electrical power of a TEG depends not only on these operating conditions, but also on the contact thermal resistance. The influence of the contact thermal resistance on the generated electrical power have already been extensively reported in the literature. However, as reported in Park et al. (Energy Convers Manag 86:233, 2014) and Montecucco and Knox (IEEE Trans Power Electron 30:828, 2015), while designing TEG-powered circuit and systems, a TEG module is mostly modeled with a Thévenin equivalent circuit whose resistance is constant and voltage proportional to the temperature gradient applied to the TEG's terminals. This widely used simplified electrical TEG model is inaccurate and not suitable under constant heat flow conditions or when the contact thermal resistance is considered. Moreover, it does not provide realistic behaviour corresponding to the physical phenomena taking place in a TEG. Therefore, from the circuit designer's point of view, faithful and fully electrical TEG models under different operating conditions are needed. Such models are mainly necessary to design and evaluate the power conditioning electronic stages and the maximum power point tracking algorithms of a TEG power supply. In this study, these fully electrical models with the contact thermal resistance taken into account are presented and the analytical expressions of the Thévenin equivalent circuit parameters are provided. [ABSTRACT FROM AUTHOR]